Problem: Simplify to lowest terms. $\dfrac{72}{48}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 48? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $48 = 2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(72, 48) = 2\cdot2\cdot2\cdot3 = 24$ $\dfrac{72}{48} = \dfrac{3 \cdot 24}{ 2\cdot 24}$ $\hphantom{\dfrac{72}{48}} = \dfrac{3}{2} \cdot \dfrac{24}{24}$ $\hphantom{\dfrac{72}{48}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{72}{48}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{48}= \dfrac{2\cdot36}{2\cdot24}= \dfrac{2\cdot 2\cdot18}{2\cdot 2\cdot12}= \dfrac{2\cdot 2\cdot 2\cdot9}{2\cdot 2\cdot 2\cdot6}= \dfrac{2\cdot 2\cdot 2\cdot 3\cdot3}{2\cdot 2\cdot 2\cdot 3\cdot2}= \dfrac{3}{2}$